Distribution functions of linear combinations of lattice polynomials from the uniform distribution

@article{Marichal2007DistributionFO,
  title={Distribution functions of linear combinations of lattice polynomials from the uniform distribution},
  author={Jean-Luc Marichal and Ivan Kojadinovic},
  journal={arXiv: Probability},
  year={2007}
}
We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice polynomials, which include weighted sums, linear combinations of order statistics, and lattice polynomials, are actually those continuous functions that reduce to linear functions on each simplex of the standard triangulation of the unit cube. They are mainly used in aggregation theory, combinatorial optimization… 

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References

SHOWING 1-10 OF 27 REFERENCES
The exact and approximate distributions of linear combinations of selected order statistics from a uniform distribution
SummaryThe exact probability density function is given for linear combinations ofk=k(n) order statistics selected from whole order statistics based on random sample of sizen drawn from a uniform
Cumulative distribution functions and moments of lattice polynomials
We give the cumulative distribution functions, the expected values, and the moments of lattice polynomials when regarded as real functions. Since lattice polynomial functions include order
Extensions of functions of 0-1 variables and applications to combinatorial optimization
For in § 2 we introduce and study “tight extensions” fD : [0, 1]n → R, defined on each n-simplex Di of a triangulation D of [0,1]n, with all vertices in {0,1}n, as the unique affine function which
LINEAR FUNCTIONS OF UNIFORM ORDER STATISTICS AND B-SPLINES
ABSTRACT The purpose of the present paper is to give a simplified method of finding the density function and the moments of linear function of order statistics from uniform distribution. This is done
Constructive Approximation
TLDR
This paper works on [-1, 1 ] and obtains Markov-type estimates for the derivatives of polynomials from a rather wide family of classes of constrained polynomes and results turn out to be sharp.
Submodular functions and convexity
TLDR
In “continuous” optimization convex functions play a central role, and linear programming may be viewed as the optimization of very special (linear) objective functions over very special convex domains (polyhedra).
Slices, Slabs, and Sections of the Unit Hypercube
Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a halfspace, or with a hyperplane of codimension 1, or with a
Approximation theory and methods
Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial
Error bounds in divided difference expansions. A probabilistic perspective
We give error bounds for the remainder term, as well as sharp upper and lower bounds for the leading term, in divided difference expansions. A main feature of this paper is the use of a probabilistic
Aggregation of interacting criteria by means of the discrete Choquet integral
The most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean. In many problems however, the criteria considered interact, and a substitute
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3
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